The homogeneous approximation is the top choice for the stability analysis for nonlinear systems when the first approximation is zero. This strategy along with the Lyapunov framework have produced several results on stability [1]}, [2]}, [3]}, robustness [4]} and controller design [5]}. The Lyapunov-Razumikhin approach has had a key role in the development of the main results on homogeneous approximations of time-delay systems: delay-independent stability [1]}, [2]}, [3]} and applications such as estimates of the solutions [1]}, [10]} and of the region of attraction [2]}. The Lyapunov-Razumikhin framework allowed establishing an outstanding result: if the delay-free system is asymptotically stable, then the trivial solution of the homogeneous delay system is asymptotically stable for all delays when the homogeneity degree is strictly greater than one [1]}.
